Definition 29.7.1. Let $X$ be a scheme. Let $U \subset X$ be an open subscheme.

1. The scheme theoretic image of the morphism $U \to X$ is called the scheme theoretic closure of $U$ in $X$.

2. We say $U$ is scheme theoretically dense in $X$ if for every open $V \subset X$ the scheme theoretic closure of $U \cap V$ in $V$ is equal to $V$.

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